Big Bob’s Pizza is having a special on pizza and is offering two different choices: Choice #1: One slice of pizza from a pizza with a 22 inch diameter and is cut into 8 slices. The cost is $4.95. Choice #2: An entire personal-size pizza that has a diameter of 6 inches. The cost is $3.75. Which choice will give you more pizza for your money? Justify your answer using numbers and words.

[tex]\bf \begin{cases} -13x=-54-20y\\ -10x=60+20y \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{-13x=-54-20y}\implies -13x+20y=-54\implies \boxed{20y}=13x-54 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 2nd equation}}{-10x=60+\left( \boxed{13x-54} \right)}\implies -10x=6+13x\implies -10x-6=13x[/tex]

[tex]\bf -6=23x\implies \blacktriangleright -\cfrac{6}{23}=x \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{-13\left( -\cfrac{6}{23} \right)=-54-20y}\implies \cfrac{78}{23}=-54-20y[/tex]

[tex]\bf \stackrel{\textit{multipying both sides by }\stackrel{LCD}{23}}{23\left( \cfrac{78}{23} \right)=23(-54-20y)}\implies 78=-1242-460y\implies 1320=-460y \\\\\\ \cfrac{1320}{-460}=y\implies \blacktriangleright -\cfrac{66}{23}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( -\frac{6}{23}~,~-\frac{66}{23} \right)~\hfill[/tex]

[tex]\bf f(x)=\stackrel{\stackrel{m}{\downarrow }}{4} x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \begin{array}{ccll} x&g(x)\\ \cline{1-2} 2&5\\4&7\\6&9 \end{array}~\hfill \begin{array}{llll} (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-5}{6-2}\implies \cfrac{4}{4}\implies \stackrel{\stackrel{m}{\downarrow }}{1} \end{array}[/tex]

well, clearly 4 > 1.

Answer:

f(x) has a greater slope.

Step-by-step explanation:

The slope of a function in the form of y=Mx+C is represented by the letter M, so the slope in the function F(x) =4.

Now when you have a function but you only have a table to evaluate it, to calculate the slope you have the next formula:

[tex]m=\frac{y^{2}- y^{1}}{x^{2} -x^{1} }[/tex]

You just have to pick two points from the table to use in the formula, we´ll use (4,7) as our point 1 and

(6,9) as our point 2.

This means that:

[tex]x^{1}=4[/tex] [tex]y^{1}=7[/tex]

[tex]x^{2}=6[/tex] [tex]y^{2}=9[/tex]

Now you just put it into the formula:

[tex]m=\frac{9-7}{6-4}[/tex]

[tex]m=\frac{2}{2}[/tex]

[tex]m=1[/tex]

Now that you have both slopes, you can see that the slope of g(x)=1 and the slope of f(x)=4, and you can see that f(x) has a greater slope thatn g(x).

Answer:

x = 1 + √6

x = 1 - √6

The two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]

From the question,

We are to determine the values of x that are roots to the quadratic equation x² +2x -5=0

Using the quadratic formula

[tex]x= \frac{-b \pm \sqrt{b^{2} -4ac} }{2a}[/tex]

From the given equation x² +2x -5=0

[tex]a = 1, \ b = 2, \ and \ c=-5[/tex]

Putting the values into the equation, we get

[tex]x= \frac{-(2) \pm \sqrt{(2)^{2} -4(1)(-5)} }{2(1)}[/tex]

This becomes

[tex]x= \frac{-2 \pm \sqrt{4 --20} }{2}[/tex]

[tex]x= \frac{-2 \pm \sqrt{4+20} }{2}[/tex]

[tex]x= \frac{-2 \pm \sqrt{24} }{2}[/tex]

Then,

[tex]x= \frac{-2 \pm 2\sqrt{6} }{2}[/tex]

∴ [tex]x= -1 \pm \sqrt{6}[/tex]

[tex]x= -1 + \sqrt{6} \ OR \ x= -1 - \sqrt{6}[/tex]

Hence, the two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]

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Answer:

The correct option is C) 4(5 + n).

Step-by-step explanation:

Consider the provided phrase.

Four times the sum of five and a number

Let the number is n and the sum of five and a number can be written as:

[tex]n+5[/tex]

Thus, four times the sum of five and a number can be written as:

[tex]4(n+5)[/tex]

Hence, the required expression is [tex]4(n+5)[/tex]

Therefore, the correct option is C) 4(5 + n).

Answer:

Isolating the x.

Step-by-step explanation:

The first step to solving this problem is to isolate the variable, x.

To do so, subtract 8x and 5 from both sides.

Step #1)

5 - 2x < 8x - 3

5 (-5) - 2x (-8x) < 8x (-8x) - 3 (-5)

-2x - 8x < -3 - 5

-10x < -8

~

Answer:

x>4/5

Step-by-step explanation:

Subtract by 5 from both sides of equation.

5-2x-5<8x-3-5

Simplify.

-2x<8x-8

Subtract by 8x from both sides of equation.

-2x-8x<8x-8-8x

Simplify.

-10x<-8

Multiply by -1 from both sides of equation.

(-10x)(-1)>(-8)(-1)

Simplify.

10x>8

Divide by 10 from both sides of equation.

10x/10>8/10

Simplify, to find the answer.

8/10=4/5

x>4/5 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

√4 * √15.

Step-by-step explanation:

√60

=√(4 * 15)

= √4 * √15

Answer:

our answer is  [tex]\sqrt{4}*\sqrt{15}[/tex] or in simplified form

as [tex]2*\sqrt{15}[/tex]

Step-by-step explanation:

[tex]\sqrt{60}[/tex]

We need to solve the above expression

Factors of 60:

1X60,  2X30, 3X20, 4X15, 5X12, 6X10

We need two factors one of which is perfect square

From the above factors only 4X15 full fills our condition as 4 is a perfect square

[tex]\sqrt{60}\\ =\sqrt{4 * 15}\\ We\,\,know\,\, \sqrt{a*b}= \sqrt{a}*\sqrt{b}\\ =\sqrt{4}*\sqrt{15}\\[/tex]

Solving, we get

[tex]2*\sqrt{15}[/tex]

So, our answer is  [tex]\sqrt{4}*\sqrt{15}[/tex] or in simplified form

as [tex]2*\sqrt{15}[/tex]

hope this helps. goodluck

Answer:

It is the last one, bc=df

The true statement is one that derives from the condition that ΔABC and

ΔDEF are congruent.

Response:

Given that the tringles are congruent, we have;

The length of the corresponding sides are equal

Similarly, the measure of the corresponding are equal

The side [tex]\mathbf{\overline{AC}}[/tex] ≅ Side [tex]\overline{DE}[/tex]

Side [tex]\mathbf{\overline{AB}}[/tex] ≅ Side [tex]\overline{EF}[/tex]

Which gives;

∠A ≅ ∠D

Given that ΔABC ≅ ΔDEF, we have;

Side [tex]\mathbf{\overline{BC}}[/tex] ≅ Side [tex]\overline{DF}[/tex]

Which gives;

∠C ≅ ∠F

Therefore;

∠B ≅ ∠D

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Answer:

 (x-2)(x-7)

Step-by-step explanation:

x2 – 9x + 14 = x² - 2x - 7x + 14

                    = x(x-2) - 7(x-2)

                    = (x-2)(x-7)

Answer:

Factor of x² – 9x + 14 is:

(x-2)(x-7)

Step-by-step explanation:

We have to find the factors of:

x² – 9x + 14

On splitting the middle term, we get

x² -7x -2x +14

which could also be written as:

x(x-7)-2(x-7)

which is equivalent to:

(x-2)(x-7)

Hence, Factor of x² – 9x + 14 is:

(x-2)(x-7)

Answer:

Step-by-step explanation:

what is the finance charge?

Answer:

n = 8.

Step-by-step explanation:

I am assuming that the sum is 255.

The last term is 128 and the common ratio is 2 so we can work backwards until we reach a sum of 255.

Term n = 128 so the previous term must be 128/2 = 64.

So following this pattern we have:

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.

So we see that n = 8.

Answer: y=6^x-3

It is a exponent form of graph, so first:

y=a^x-b

When b=0, the asymptote is y=0 but as the asymptote given is y=-3, b=-3

Second:

the y value increases 6, when x changes 0 to 1, so a=6

[tex]n^2=\dfrac{1}{16}\\\\n=-\dfrac{1}{4} \vee n=\dfrac{1}{4}[/tex]

Answer:

0.66666666666666666 ( goes on forever )

Step-by-step explanation:

This simplifies to 2/3, which is known to be 0.666666666666 and so on.

Answer:

0.66666667

Step-by-step explanation:

The numbers just keep going on and on and on, but the 7 in the number stops it.

Answer:

n=m(x)

Step-by-step explanation:

n is the dependent variable m is the independent variable.

how many cartons, depends on how many liters are in a carton.

how many he needs to buy= the amount in carton× how ever much is in his recipe

for example

if they're are let's say 1.5 liters per carton than m=1.5. and if he needs 15 liters than n= 15

than the equation is

[tex]15 = 1.5 \times x[/tex]

x is how many cartons he needs to buy

solve for x by dividing both sides of the equation by 1.5

[tex]15 \div 1.5 = x[/tex]

and x=10 in this scenario

Answer:

A

Step-by-step explanation:

The answer would be E and G. Points E and G are both OUTSIDE both circles

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

2

Step-by-step explanation:

Center: (−4,3)

Radius: 2

Answer:

radius = 2

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

Given

x² + y² + 8x - 6y + 21 = 0

Use the method of completing the square to obtain standard form

Collect the x- terms and y- terms together and subtract 21 from both sides

x² + 8x + y² - 6y = - 21

add ( half the coefficient of the x/y terms )² to both sides

x² + 2(4)x + 16 + y² + 2(- 3)y + 9 = - 21 + 16 + 9

(x + 4)² + (y - 3)² = 4 ← in standard form

with centre (- 4, 3) and radius = [tex]\sqrt{4}[/tex] = 2

Answer:

f(x)^-1 = 1/3x - 2

Step-by-step explanation:

Replace f(x) with y and solve:

y = 3x + 6

Swap x and y

x = 3y + 6

Now isolate y

x/3 = 3y/3 + 6/3

1/3 x = y + 2

1/3 x - 2 = y + 2 - 2

y = 1/3x - 2 or f(x)^-1 = 1/3x - 2

For this case we have the following function:

[tex]f (x) = 3x + 6[/tex]

We must find the inverse of the function, then:

Replace f (x) with y:[tex]y = 3x + 6[/tex]

We exchange the variables:

[tex]x = 3y + 6[/tex]

We solve for "y":

Subtracting 6 on both sides of the equation:

[tex]x-6 = 3y[/tex]

Dividing between 3 on both sides of the equation:

[tex]y = \frac {x} {3} - \frac {6} {3}\\y = \frac {x} {3} -2[/tex]

We change y by [tex]f ^ {- 1} (x)[/tex], and finally we have:

[tex]f ^ {- 1} (x) = \frac {x} {3} -2[/tex]

ANswer:

[tex]f ^ {- 1} (x) = \frac {x} {3} -2[/tex]

Option D which simplifies to 11y +17 = 11y -10 has no solution since the left and right sides of the equations aren't equal after simplifying.

We are tasked with determining which equation has no solution among the given options: A) 13y + 2 - 2y = 10y + 3 - y, B) 9(3y +7) - 2 = 3(-9y + 9), C) 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1 and D) 5(2.2y + 3.4) = 5(y - 2) + 6y. The equation without a solution will be the one in which the variables cancel out and the remaining numbers are not equal.

Solving the equations, starting with A, by combining like terms, we have 11y + 2 = 9y + 3, this eventually gives us y = 0.5.  Option B, simplifying gives us 27y + 63 = -27y + 27, therefore y = -1.33. For C, we simplify to 34.5y + 3.1 = 34.5y - 5.1. Because both sides of the equation have equal coefficients for y, this results in 34.5y = 34.5y, which holds true for any value of y. Hence, the equation has infinitely many solutions. Option D simplifies to 11y +17 = 11y -10. Here, we see that 11y = 11y is true, however, the constants are not equal (i.e. 17 does not equal -10). Thus, option D is the equation with no solution.

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Answer:

205/6

Step-by-step explanation:

The question simply asks us to plug in 45 minutes into the given equation. In the graph, we see that y-axis is defined to be time. Therefore we set y=45 and solve for x.

45=-6/5x+86

-41=-6/5x (subtract 86 from both sides)

-41*(-5)=-6/5x*(-5) (multiply both sides by -5)

205=6x (divide both sides by 6)

205/6=x

Answer:

change of y/ change of x

Step-by-step explanation:

Answer:

C) Domain: -3, -1, 0, 3

Range: -1, 0, 1, 2, 3

Step-by-step explanation:

Domain is using x values

Range is using y values

[tex]\textbf{Answer:}[/tex]

[tex]\frac{-1}{4}[/tex]

[tex]\textbf{Step-by-step explanation:}[/tex]

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

[tex]\textrm{Use the formula above to determine the rate of change}[/tex]

[tex]\frac{1 - 2}{4 - 0} \rightarrow\frac{-1}{4}[/tex]

[tex]\textrm{The rate of change of this line is }[/tex] [tex]\frac{-1}{4}[/tex]

recall that all we need is two points off a straight line to get its slope, so... hmmm this one passes through (0 , 2) and (4 , 1), so let's use those

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{4-0}\implies -\cfrac{1}{4}[/tex]

Answer:

choice number 2) 10 in, 18.5 in 31.5 in

Step-by-step explanation:

we collect and evaluate the like terms.like terms means the ones that can be evaluated. like 2y and 7y are like terms. they either can be added or subtracted to get an answer . 7y-2y =5y. but you cant subtrac or add 7y  with 5 because they are not like terms.

2y +1 + 7y + 3y + 5 = 60

(2y+7y+3y)+(1+5) = 60

12y + 6 = 60

The 6 crosses the equal sign to the other side because of like terms.And becomes a minus

12y = 60 - 6

12y = 54

y = 4.5

so,

2y +1= 2 x 4.5 + 1 =10

7y = 7 x 4.5 = 31.5

3y + 5= 3 x 4.5 + 5 =18.5

Answer is 10 in, 18.5 in, 31.5 in

If you need any clarification or more explanation pls do mention at the comment section so that i can help more thx

Hope this helps and if it does pls mark as branliest answer thx

Answer:

[tex]b=200(1.04)^{d}[/tex]

Step-by-step explanation:

we know that

The exponential function is of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

In this problem we have

a=200 birds

b=100%+4%=104%=104/100=1.04

substitute

[tex]y=200(1.04)^{x}[/tex]

Let change of variables

[tex]b=200(1.04)^{d}[/tex]

where

b is the amount of birds in the flock

d is the number of days since the 200 birds started

The set of coordinates which paired with (-3,-2) and (-5,-2) are (-4,0) and (-4,0).

The coordinates are the points with the help of which we can draw any figure on the graph.

We know that all the sides of a square are equal to each other.

Let ABCD be a square.

Coordinates of A(-3,-3) and C be(-5,-2)

Let the coordinates of B and D be (x1,y1) and (x2,y2)

To be a square AB=CD=BC=AD

AB=BC

[tex]\sqrt{(x1+3)^{2}+(y1+2)^{2} }[/tex]=[tex]\sqrt{(-5-x1)^{2} +(-2-y1)^{2} }[/tex]

solving this we will find

x1=-4

because y1 is not in the solution so y1 be equal to 0.

AD=DC

[tex]\sqrt{(-5-x2)^{2} +(-2-y2)^{2} }[/tex]=[tex]\sqrt{(x2+3)^{2} +(y2+2)^{2} }[/tex]

solving this we will find x2=-4 and y2=0

Hence the coordinates are (-4,0),(-4,0)

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Final answer:

The coordinates that form a square when paired with (-3, -2) and (-5, -2) are (-3, 0) and (-5, 0). The sides of the square are 2 units long, and by moving perpendicularly up by 2 units from each given point, we find the other two vertices of the square.

Explanation:

The student has asked which set of coordinates, when paired with (-3, -2) and (-5, -2), would result in a square. To find the coordinates that complete the square, we need to consider that the diagonals of a square are equal in length and bisect each other at right angles. The two given points (-3, -2) and (-5, -2) form a side of the square that is parallel to the x-axis and 2 units long. Since a square has all sides equal, the other two vertices of the square will be 2 units away from these points but in a perpendicular direction.

Here's how we calculate it step by step:

First, we determine the length of the side of the square by calculating the distance between the points (-3, -2) and (-5, -2), which is 2 units.

Next, we move 2 units perpendicularly from each point which can be done by either keeping the x-coordinate constant and changing the y-coordinate or vice versa. Since we want to be perpendicular to the x-axis, we change the y-coordinate.

The change in the y-coordinate could be either upwards (+2) or downwards (-2). Considering the y-value of the given points, one possible set of coordinates for the other two vertices are (-3, 0) and (-5, 0).

Therefore, the coordinates (-3, 0) and (-5, 0), when paired with (-3, -2) and (-5, -2), form a square.

Answer:

Step-by-step explanation:

% = (sucesses / attempts) * 100

% = (47/65) * 100

% = 0.723 * 100

% = 72.3 %

Answer: 72.3%  

Step-by-step explanation:

Given statements : The number of basketball games = 14

The number of free throws attempted = 65

The number of made = 47

Now, the experimental probability that you make a free throw is given by :-

[tex]\dfrac{\text{47}}{65}=0.72307\approx0.723[/tex]

In percent , [tex]0.723\times100=72.3\%[/tex]

Hence, the  experimental probability that you make a free throw =72.3%  

Answer:

12.5698 (approximately 12.5, rounding to the nearest half)

Step-by-step explanation:

The area of a square is represented by the following equation:

[tex]A=a^2[/tex]

Whereas "a" represents the length of any one of the sides.

Since all sides of a square are equal in length, we can reverse engineer this formula to find the length of one side.

[tex]158=a^2[/tex]

Simply take the square root of both sides and you will have your answer.

[tex]12.5698=a[/tex]

To determine the length of one side of a square sign with an area of 158 feet, calculate the square root of the area which is approximately 12.57 feet.

A square sign has an area of approximately 158 feet. To find the length of one side of the sign, you need to calculate the square root of the area:

Side length = √(Area)

Side length = √(158) = 12.57 feet

Answer:

13 is the answer.

Step-by-step explanation:

In this question the given fraction is

Now we have to simplify the fraction to the nearest integer.

Since the integers are whole number not in fraction therefore 12.5 can be written as 13 as the nearest integer.

Step-by-step explanation:

Please mark brainliest and have a great day!

To find 1,242 divided by 99 and rounded to the nearest integer, we do the division and then round the result. The result of the division is 12.545..., and when rounded to the nearest integer, we get 13.

The question is asking us to divide 1,242 by 99 and round the result to the nearest integer. First, we do the division: 1,242 ÷ 99 = 12.545454545.... Since we need to round to the nearest integer, we look at the digits following the decimal point. Because the digit immediately after the decimal point is 5 or more, we round up the integer part. So, 1,242 ÷ 99 rounded to the nearest integer is 13.

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Answer:

20000*(0.85)^x

Step-by-step explanation:

Answer:

The function f(x) representing the value of car after x years is given by

[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]

Step-by-step explanation:

Since value of car depreciates by 15% each year

Value of car after 1 year

[tex]f(1)=value of new car \times(1-\frac{15}{100})[/tex]

=>[tex]f(1)=\$ 20,000\times(1-\frac{15}{100})[/tex]

Value of car after 2 year

[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]

=>[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})^{2}[/tex]

Value of car after 3 year

[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]

=>[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})^{3}[/tex]

Similarly value of car after x years is

[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]